바로가기메뉴

본문 바로가기 주메뉴 바로가기

ACOMS+ 및 학술지 리포지터리 설명회

  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
  • 2024년 07월 03일(수) 13:30
사전등록 바로가기
 

logo

ISSN : 1226-0657

논문 상세

다음
논문 투고

Vol.20 No.4
Citation Share

CERTAIN CLASSES OF INFINITE SERIES DEDUCIBLE FROM MELLIN-BARNES TYPE OF CONTOUR INTEGRALS

CERTAIN CLASSES OF INFINITE SERIES DEDUCIBLE FROM MELLIN-BARNES TYPE OF CONTOUR INTEGRALS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2013, v.20 no.4, pp.233-242
https://doi.org/10.7468/jksmeb.2013.20.4.233
Choi, Junesang (Department of Mathematics, Dongguk University)
Agarwal, Praveen (Department of Mathematics, Anand International College of Engineering)
Choi, Junesang, & Agarwal, Praveen. (2013). CERTAIN CLASSES OF INFINITE SERIES DEDUCIBLE FROM MELLIN-BARNES TYPE OF CONTOUR INTEGRALS. 한국수학교육학회지시리즈B:순수및응용수학, 20(4), 233-242, https://doi.org/10.7468/jksmeb.2013.20.4.233
  • 다운로드 수
  • 조회수
PDF 다운로드

Abstract

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function <TEX>${\psi}(z)$</TEX>, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving <TEX>${\psi}(z)$</TEX>. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving <TEX>$\bar{H}$</TEX>-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving <TEX>${\psi}(z)$</TEX>. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

keywords
gamma function, Pochhammer symbol, Psi (or Digamma) function, generalized hypergeometric function <tex> $_pF_q$</tex>, H-function, <tex> $\bar{H}$</tex>-function, Mellin-Barnes type of contour integral

참고문헌

1.

(1991). A certain family of infinite series associated with Digamma functions. J. Math. Anal. Appl., 159, 361-372. 10.1016/0022-247X(91)90200-J.

2.

(1995). Fractional calculus and the sums of certain families of infinite series. J. Math. Anal. Appl., 190, 738-754. 10.1006/jmaa.1995.1107.

3.

(1964). Asymptotic expansions and analytic continuations for a class of Barnes-integrals. Compositio Math., 15, 239-341.

4.

(1990). The H-function associated with a certain class of Feyman integrals. J. Phys. A: Math. Gen., 23, 4707-4710. 10.1088/0305-4470/23/20/030.

5.

(2000). Some infinite series and functional relations that arose in the context of fractional calculus. J. Math. Anal. Appl., 252, 376-388. 10.1006/jmaa.2000.7079.

6.

(1987). New properties of hypergeometric series derivable from Feynman integrals: I. Transformation and reduction formulae. J. Phys. A. : Math. Gen., 20, 4109-4117. 10.1088/0305-4470/20/13/019.

7.

(1987). New properties of hypergeometric series derivable from Feynman integrals: II. A generalisation of the H function. J. Phys. A.: Math. Gen., 20, 4119-4128. 10.1088/0305-4470/20/13/020.

8.

(1989). Certain classes of infinite series summable by means of fractional calculus. J. College Engrg. Nihon Univ. Ser. B, 30, 97-106.

9.

(1997). A new generalization of generalized hypergeometric functions. Le mathematiche Fasc. II, 52, 297-310.

10.

(1998). Functional relations involving generalized H-function. Le Mathematiche Fasc. I, 53, 123-131.

11.

(2002). Applications of generalized H-function in bivariate distributions. Rew. Acad. Canar. Cienc. XIV, (1-2), 111-120.

12.

(1992). A simple algorithm for the evaluation of a class of generalized hyper-geometric series. Stud. Appl. Math., 86, 79-86.

13.

(1992). An elementary proof of a generalization of certain functional relation. J. Fractional Calculus, 1, 69-74.

14.

Zeta and q-Zeta Functions and Associated Series and Integrals.

15.

(1991). A simplified overview of certain relations among infinite series that arose in the contex of fractional calculus. J. Math. Anal. Appl., 162, 152-158. 10.1016/0022-247X(91)90183-Z.

16.

Series Associated with the Zeta and Related Functions.

한국수학교육학회지시리즈B:순수및응용수학

논문 투고 OA 정책